Further Mathematics (A Level)

At Heathfield Further Mathematics is offered as part of our Double Mathematics Course. As a College the structure of this curriculum should allow for students to be fully prepared for the demands of Further Mathematics and have a secure foundation of knowledge from the A Level Mathematics Curriculum.

The Double Mathematics course comprises of two A Levels: Mathematics and Further Mathematics. Students will study for A Level Mathematics in Year 1, and sit the exams for this in the summer term. In Year 2 students will study for Further Mathematics, having already gained an A Level in Mathematics. In both years students will have double the curriculum time compared to other courses to allow for the completion of a whole A Level in one year.

Please read the A Level Mathematics course information alongside the details below.

What you will learn

In Further Mathematics, the course begins looking at the key concepts of complex numbers and matrices. Many of the topics learnt the previous year in Mathematics, such as trigonometry, calculus, series, vectors and proof, are explored at a deeper and and more complex level. Brand new concepts such as number theory, group theory and power series are introduced.

How you will learn

Topics will be taught in a natural progression that will allow previous learnt skills to be applied and built upon. Much of the learning in mathematics comes through practise and rigour. Once a new topic has been learnt in class, deep understanding and mastery is developed through smart exercises and assessments.

Year 1

During Year 1 students will complete the A Level Mathematics Specification. Please see the course guide for A Level Mathematics for information.

Year 2

Core Pure Mathematics:

• Complex Numbers
• Solving cubic and quartic equations
• Argand diagrams
• Series formuale – sum of natural numbers, squares and cubes
• Roots of polynomials
• Volumes of revolution
• Matrices
• Solving systems of equations using matrices
• Linear transformations with matrices
• Proof by induction
• Vector equations of lines and planes
• Scalar product
• De Moivre’s Theorem
• nth roots of complex numbers
• Method of differences
• Maclaurin Series
• Improper integrals
• Mean Value of a function
• Further integration techniques
• Polar coordinates
• Polar functions
• Hyperbolic functions
• Calculus with hyperbolic functions
• First-order differential equations
• Second-order differential equations
• Simple harmonic motion
• Damped and forced harmonic motion
• Systems of first-order differential equations

Further Pure Mathematics 1:

• Vector product
• Scalar triple product
• Parabolas
• Ellipses
• Hyperbolas
• Eccentricity
• Solving inequalites where x is a denominator
• Modulus inequalites
• The t-formulae
• Taylor Series
• Leibnitz’s Theorem
• L’Hôpitals rule
• The Weierstrauss substitution
• Simpson’s Rule
• Reducible differential equations

Further Pure Mathematics 2:

• Euclidian algorithm
• Modular arithmetic
• Congruence Equations
• Fermat’s little theorem
• Combinatronics
• Group Theory
• Cayley tables
• Isomorphism
• Loci in Argand Diagrams
• Transformations of the complex plane
• Recurrence relations
• Proving closed forms
• Eigenvalues and eigenvectors
• Cayley-Hamilton theorem
• Reduction formulae
• Arc length and surface areas of revolution

The assessments below are for Further Mathematics completed at the end of Year 13

Assessment 1. Core Pure Mathematics 1, written examination, 1 hour 30 minutes, 25% of final grade.

The examination will be based around the following topics:

Inductive Proof, Complex numbers, Matrices, Further calculus techniques, Series, Volumes of revolution, Polar coordinates and functions, Hyperbolic functions, Differential Equations

Assessment 2. Core Pure Mathematics 2, written examination, 1 hour 30 minutes, 25% of final grade

The examination will be based around the following topics:

Inductive Proof, Complex numbers, Matrices, Further calculus techniques, Series, Volumes of revolution, Polar coordinates and functions, Hyperbolic functions, Differential Equations

Assessment 3. Further Pure Mathematics 1, written examination, 1 hours 30 minutes, 25% of final grade.

The examination will be based around the following topics:

Vectors, Conic sections, Inequalities, t-formulae, Taylor Series, Further calculus, Differential Equations

Assessment 4. Further Pure Mathematics 2, written examination, 1 hour 30 minutes

The examination will be based around the following topics:

Number Theory, Group Theory, Complex numbers and loci, Recurrence relations, Matrix algebra, Surface areas of revolution

College basic entry requirements

• Grade 7 or above in GCSE Mathematics

Where Next?

Always impressive on UCAS applications, Further Mathematics marks students out as extremely capable mathematicians. Should a student have a desire to study mathematics or engineering in higher education, Further Mathematics is often listed as a desirable or compulsory entry requirement for these courses at top universities.

In addition to specific skills and knowledge, the Further Mathematics course develops the ability to think clearly and logically through problems and as such is a widely respected qualification.

Course Combinations

The course combines well with Computer Science, Chemistry, Biology, Physics, and Business.